Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e6 + 10;
const int MOD = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int num;
  cin >> num;
  vector<int> tri(44721);
  for (long long i = 1;; i++) {
    if (i * (i + 1) / 2 > MOD) break;
    tri[i - 1] = i * (i + 1) / 2;
  }
  int n = tri.size();
  for (int i = 0; i < n; i++) {
    for (int j = 0; j <= i; j++) {
      if (tri[i] + tri[j] == num) {
        cout << "YES";
        return 0;
      }
      if (tri[i] + tri[j] > num) break;
    }
    if (tri[i] > num) break;
  }
  cout << "NO";
}